How analogies both save us - and fail us
Written in my hotel in Seattle, polished on AA7158 flying Seattle to San Jose and dispatched to silicon.com via a free LAN service provided by my San Jose hotel.
All my life I have found visual images, real and imaginary, absolutely vital to my understanding of most complex things. I'm not sure when I became aware of my own need for such augmentation but it started to become apparent as the nature and quality of my education accelerated away from the early school system.
From the movement of electrons to the action of electro-magnetic waves, sound and photons, pictures played a vital role in linking theory and practice. And as my own professional life developed and I too had the pleasure of teaching others, I actively sought out vivid analogies to fit every situation I found students struggling with.
I can claim no credit for this line of approach, as my own teachers imparted so much clarity by the same mechanism. Curiously the more complex a topic the better my teachers seemed to be at the art of mental visualisation. In fact my early understanding of the physical world was entirely limited by the poor artistry and imagination of my schoolteachers.
In some ways it seemed unfortunate that the converse was not true - that the best visualisers weren't available much earlier in the process. If it were so I believe that far more people would be able to grasp the mechanisms that govern our lives and environment.
So it was with some pleasure, and more than a smile, that this week I sat before a presenter who painted a graphic picture of a mathematical process that stumps many. It was a hash function, which can be used in cryptography and other areas such as data correlation. The requirements are typically stated as:
- The input can be of any length
- The output has a fixed length
- The function H(x) can be computed for any given x
- H(x) is one-way
- H(x) minimises collisions
This was skillfully reduced down to a piglet, a sausage and a grinder!
Put the piglet in the grinder and you get a sausage but there is no way back - it is irreversible! And of course, putting different animals in the grinder just produces different kinds of sausage - they are all different and all irreversible.
That's it! As clean and concise a description as you could ask for, and certainly one I shall remember, recall and use, along with many more I have picked up along my many years of continuing education.
Of course no analogy, and certainly no picture, is an absolute and correct representation of the truth. In fact the simplification of an analogy is generally afforded at the direct expense of truth. This is something I refer to as the lie curve (See figure below). If we tell the absolute truth then the understanding often comes at a high price. But if we over-simplify by analogy, then the truth is quickly bastardised and the recipient is left with the illusion of a distorted and partial knowledge.
So is this true of the piglet and the grinder? Sort of! But only through technology that doesn't quite exist yet. In the not too distant future we may find ourselves in a position to invoke genetics and proteomic technologies, or even a nano-tech rebuild, to reverse engineer the atoms of a sausage into a piglet.
Too wild a thought? Then how about a quantum computer working on a series of hash values, attempting every single combinatorial possibility, in almost zero time, and decoding the original input? Even worse perhaps?
How could this possibly work? Well it is kind of complex, might require more energy than we currently imagine, and until we actually have these technologies, which might take another 50 years, we cannot know for sure. So in the meantime we have to content ourselves with models, speculation and, of course, even more analogies!